The reflection image is usually considered as a blurred version of the reflected scene due to the effect of the glass.
With different characteristics, \(\mathbf {T}\)  and \(\mathbf {R}\)  are assumed to have two different representations over a transmission dictionary \(\mathbf {D}_T\)  and a reflection dictionary \(\mathbf {D}_R\) , respectively.
Based on the Convolutional Sparse Coding (CSC) model [1]}, [2]}, we propose to formulate the reflection removal problem as:
\(\begin{aligned}\underset{\mathbf {z}_T, \mathbf {z}_R}{\min } & \frac{1}{2} \Vert \mathbf {I} - \sum _{i=1}^N \mathbf {D}_T^i \otimes \mathbf {z}_T^i - \sum _{j=1}^N \mathbf {D}_R^j \otimes \mathbf {z}_R^j \Vert _F^2 + \lambda _T p_T(\mathbf {z}_T) + \lambda _R p_R(\mathbf {z}_R),\end{aligned}\) 
